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Knee osteoarthritis (OA) is a common degenerate joint disorder that affects a large population of elderly people worldwide. Accurate radiographic assessment of knee OA severity plays a critical role in chronic patient management. Current clinically-adopted knee OA grading systems are observer subjective and suffer from inter-rater disagreements. In this work, we propose a computer-aided diagnosis approach to provide more accurate and consistent assessments of both composite and fine-grained OA grades simultaneously. A novel semi-supervised learning method is presented to exploit the underlying coherence in the composite and fine-grained OA grades by learning from unlabeled data. By representing the grade coherence using the log-probability of a pre-trained Gaussian Mixture Model, we formulate an incoherence loss to incorporate unlabeled data in training. The proposed method also describes a keypoint-based pooling network, where deep image features are pooled from the disease-targeted keypoints (extracted along the knee joint) to provide more aligned and pathologically informative feature representations, for accurate OA grade assessments. The proposed method is comprehensively evaluated on the public Osteoarthritis Initiative (OAI) data, a multi-center ten-year observational study on 4,796 subjects. Experimental results demonstrate that our method leads to significant improvements over previous strong whole image-based deep classification network baselines (like ResNet-50)., Comment: extension of RSNA 2020 report "Consistent and Coherent Computer-Aided Knee Osteoarthritis Assessment from Plain Radiographs"